The straight line y=x+3 cuts the circle x^2+y^2-6x-4y-3=0 at points P and Q, where Q lies in the first quadrant.
Calculate the coordinates of P and Q. Then, state the coordinates of the point of intersection of the tangents to the circle at points P and Q.
The midpoint of PQ is the vertex of a parabola with its axis parallel to the y-axis. Given that the parabola also passes through the point P, find the equation of the parabola and state the coordinates of its focus.